Wsan restoration method using forced base calculation

ABSTRACT

The method is based on a distributed dropping approach which introduces minimal disruption to previously deployed mobile nodes, and decreases total travelled distance a mobile node might move compared with a traditional central dropping approach. Thus, the distributed dropping approach can expedite the restoration process, reduce power consumption, and expand survival time of a WSAN.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Wireless sensor and actor networks (WSANs) refer to a group of sensornodes and actor nodes wirelessly linked to perform distributed sensingand acting tasks. In one example of WSANs, sensor nodes collectinformation from their surrounding environment and transmit sensor datato actor nodes, while the actor nodes collaboratively make decisionsbased on the collected information and take actions upon theenvironment. WSANs can be applied in various fields, such as spaceexploration, combat field reconnaissance, border protection, search andrescue, and the like.

Upon their deployment, nodes of WSANs are expected to stay connectedwith each other and form a network. Network connectivity enables nodesto coordinate their action while performing a task, and to forward theirreadings, for example, to a base-station that serves as a gateway toremote control centers. However, WSANs are prone to node failures. Forexample, a node may fail due to an external damage caused by, forexample, natural disasters, or because of hardware malfunction, batterydepletion or improper initial deployment. In some applications, WSANsoperating in a harsh environment may suffer from large scale damagewhich partitions the network to disjoint segments. For example, in abattle field, pans of the deployment area may be bombed, and nodes inthe vicinity would be destroyed and surviving nodes can be split intodisjoint partitions (segments). Losing connectivity between partitionedsegments prevents data exchange and coordination among some nodes.Therefore, restoring the overall network connectivity is crucial.

The existing solutions for restoring connectivity of partitioned WSANscan be categorized into two categories: self-healing approaches thatexploit the existing actor nodes to restore the network connectivity,and relay-based approaches that use external actor nodes in order torestore connectivity.

The self-healing approaches reconnect the separated partitions byreducing the distance between surviving nodes below their transmissionrange, so it does not require extra node deployment. However, theself-healing approaches require mobility of some nodes, which mayincreases the cost and adds an extra complexity to the hardware, inaddition to high energy consumption for long distance travelling. Theself-healing approaches can be subcategorized into centralizedapproaches and distributed approaches. In centralized approaches, theinformation about remaining undamaged nodes can be collected possibly bya server which performs the selection of the nodes to move and theirfinal destination, to assure connectivity. The distributed approach doesnot require complete information about the damage and the partitions.

The relay-based approaches restore connectivity among segments bydeployment of additional relay nodes (mobile nodes). Some solutionsbased on the relay-based approaches may require information about thedamaged area, the number of network partitions and the location of theremaining nodes. However, that information may be inaccurate or may notbe obtained for some applications where access to the damaged area isimpractical due to difficult or dangerous scenarios, such as gasleakage, forest fire, or geographical difficulties (e.g., Amazon forestor active volcanoes). Thus, the relay nodes self-deployment strategiesare needed for applications where accurate information of partitionedWSANs is not available.

SUMMARY

Aspects of the disclosure provide a method for restoring connectivityamong partitioned segments in a partitioned wireless sensor and actornetwork (WSAN). The method includes placing batches of mobile nodes atlocations surrounding mobile nodes previously placed within a damagedarea of the partitioned WSAN, spreading the batches of mobile nodes,determining whether connectivity among the partitioned segments has beenrestored, and repeating placing batches of mobile nodes, spreading thepatches of mobile nodes, and determining whether connectivity among thepartitioned segments has been restored when connectivity among thepartitioned segments is not restored.

The method is based on a distributed dropping approach which introducesminimal disruption to previously deployed mobile nodes, and decreasestotal travelled distance a mobile node might move compared with atraditional central dropping approach. As a result, the distributeddropping approach can expedite the restoration process, reduce powerconsumption, and expand survival time of a WSAN.

In an example, the locations surrounding previously placed mobile nodesare within a transmission range of the previously placed mobile nodes.

An embodiment of the method further includes placing batches of mobilenodes at locations surrounding previously placed mobile nodes butexcluding locations where a partitioned segment is connected to themobile nodes previously placed within the damaged area of thepartitioned WSAN.

In one example, the method further includes placing an initial batch ofmobile nodes at an initial location within a damaged area of the WSAN.In another example, the method further includes placing first batches ofmobile nodes at locations on a first circle centered at the initiallocation with a first radius, and placing second batches of mobile nodesat locations on a second circle centered at the initial location with asecond radius that is larger than the first radius. In a furtherexample, the method further includes placing a first batch of mobilenodes at a first location surrounding the mobile nodes previously placedwithin the damaged area of the partitioned WSAN, spreading the firstbatch of mobile nodes, and placing a second batch of mobile nodes at asecond location surrounding the mobile nodes previously placed withinthe damaged area of the partitioned WSAN. In an even further example,the method further includes spreading the batches of mobile nodesaccording to a force based algorithm (FBA).

Aspects of the disclosure provide a method for placing mobile nodes torestore connectivity among partitioned segments in a partitioned WSAN.The method includes placing an initial batch of mobile nodes at aninitial location within a damaged area of the partitioned WSAN, placingbatches of mobile nodes at locations surrounding previously placedmobile nodes that are previously placed within a damaged area of thepartitioned WSAN, and repeating placing batches of mobile nodes atlocations surrounding previously placed mobile nodes until connectivityamong partitioned segments is restored.

Aspects of the disclosure provide a method for spreading mobile nodesdropped for restoring connectivity among partitioned segments in apartitioned WSAN. The method includes receiving, at a mobile node,location information from neighboring nodes, calculating a net repulsiveforce that is imposed on the mobile node and includes a sum of repulsiveforces from the neighboring nodes within a threshold distance from themobile node, calculating a net movement distance based on the netrepulsive force imposed on the mobile node determining a location basedon the net movement distance when the net movement distance is smallerthan the transmission range, or based on a restricted movement distancerestricted to a transmission range of the neighboring nodes when the netmovement distance is larger than the transmission range, and moving themobile node to a location determined based on the calculated restrictedmovement distance.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of this disclosure that are proposed as exampleswill be described in detail with reference to the following figures,wherein like numerals reference like elements, and wherein:

FIG. 1 shows an example of a partitioned wireless sensor and actornetwork (WSAN);

FIG. 2 shows an exemplary flowchart of a process for spreading thedeployed mobile nodes based on a force based approach;

FIG. 3 shows an example of a mobile node placement process utilizing thedistributed dropping algorithm;

FIG. 4 shows a polar representation of a process of dropping batches ofmobile nodes;

FIG. 5 shows an example of an algorithm (in the form of pseudocode) forrestoring disjoint segments in the WSAN; and

FIG. 6 shows an example of a process for restoring connectivity in apartitioned WSAN.

DETAILED DESCRIPTION OF EMBODIMENTS

I. Example of Partitioned Wireless Sensor and Actor Networks (WSANs)

FIG. 1 shows an example of a partitioned WSAN 100. The WSAN 100initially includes a plurality of sensor nodes and actor nodes that arerandomly deployed into an application area 101. However, due to nodefailures, for example, caused by a natural disaster, the WSAN 100 ispartitioned into four isolated segments 110 a-110 d. Nodes in damagedarea 160 stop to operate, while nodes 120 within each segment 110 a-110d can operate properly and communicate with each other directly or viaother nodes of the same segment, thus forming portioned sub-networks. Inaddition, nodes 120 within each segment 110 a-110 d can include nodesunable to move (e.g., a sensor without moving ability) and nodes able tomove (e.g., a robotic actor with moving ability), but nodes 120 withineach segment 110 a-110 d remain stationary after being partitioned. TheWSAN 100 can also include a base station 130 which serves as a gatewayproviding a communication channel between the WSAN 100 and a controlcenter (not shown). Through the based station 130, sensor data can betransmitted to the control center for further processing, and controlcommand can be transmitted to nodes of the WSAN 100.

After the partition of the WSAN 100 is detected, for example, by thebase station 130, a restoration process can be initiated. As shown inFIG. 1 example, a deployment vehicle 150 can be employed to deployadditional mobile nodes 140 to the damaged area 160. The deploymentvehicle 150 can be a robot, an unmanned aerial vehicle (UAV), and thelike. The mobile nodes 140 can include positioning circuitry todetermine its location, and wireless communication circuitry to exchangelocation information among the mobile nodes 140.

During the restoration process, multiple batches of mobile nodes 140 canbe sequentially placed to certain different locations. One way formobile node placement (referred to as central dropping approach) is todrop batches of mobile nodes 140 at a same location near the center ofthe damaged area 160, and the dropped mobile nodes then spread tolocations close to the partitioned segments 110 a-110 d in order toreach the segments 110 a-110 d.

According to an aspect of the disclosure, in some examples, adistributed dropping approach for mobile node placement is adoptedinstead of dropping mobile nodes at a central location within thedamaged area. Specifically, in an example of the distributed mobile nodeplacement approach, a first batch of mobile nodes can be placed at acentral location of the damaged area 160, and subsequent batches ofmobile nodes can be placed around the previously deployed mobile nodes,for example, on a circle surrounding the previously deployed mobilenodes and in different directions from the central location. Thedistributed dropping approach introduces minimal disruption topreviously deployed mobile nodes, and decreases total travelled distancea mobile node might move compared with the central dropping approach. Asa result, the distributed dropping approach can expedite the restorationprocess, reduce power consumption, and expand survival time of a WSAN.

II. Force Based Algorithm (FBA) for Spreading Deployed Mobile Nodes

In some examples, batches of deployed mobile nodes 140 spread over thedamaged area 160 in order to reconnect the disjoint segments 110 a-110 dof the partitioned WSAN 100, and the spreading process utilizes a forcebased algorithm (FBA). In the FBA, each mobile node 140 is assumed to bepolarized with a same magnetic pole, and impose virtual repulsive forcesupon each other based on the principle of magnetic repelling forces inphysics. For example, initially, some batches of mobile nodes 140 havebeen deployed and spread over the damaged area 160. Then, one or morebatches of mobile nodes 140 are placed at certain locations nearpreviously deployed mobile nodes 140. The newly deployed mobile nodes140 of the same batch are close to each other. In addition, the newlydeployed mobile nodes 140 are also close to the previously droppedmobile nodes 140. As a result, the mobile nodes 140, newly or previouslydeployed, apply repulsive forces to each other.

FIG. 2 shows a flowchart of a process 200 for spreading the deployedmobile nodes 140 based on the FBA. The process 200 can be performed by amobile node 140 dropped at the damaged area 160 in the FIG. 1 example.The process 200 starts at S201 and proceeds to S210.

At S210, location information is received from neighboring nodes at amobile node Ni. In one example, some batches of mobile nodes 140 arenewly deployed, and a spreading process is initiated to move the mobilenodes 140 to locations close to the disjoint segments 110 a-110 d. Inanother example, after batches of mobile nodes 140 are newly deployed, aspreading process has been performed for several iterations, and newmovement locations need to be determined for a new iteration. In orderto determine the movement locations, location information of neighboringnodes needs to be exchanged among the deployed mobile nodes 140. Theneighboring nodes can include deployed mobile nodes 140 and thestationary nodes 120 in the segments 110 a-110 d.

In an example, each node of the WSAN (mobile nodes 140 or stationarynodes 120) can include positioning circuitry, such as a GPS receiver,that generates location information of the respective mobile node. Inaddition, each node 140/120 can include wireless communication circuitryenabling message exchanges among the nodes 140/120. Thus, a node 140/120can receive a message from its neighboring nodes 140/120 carryinglocation information of each respective neighboring node 140/120.

In addition, message exchanged between two nodes 140/120 may beunsuccessful due to the effect of wireless channel corruption betweenthe nodes 140/120 (e.g., fading or shadowing experienced fromsurrounding environment). In some examples, when one node 140/120 cannotreceive messages from a neighboring node, the node 140/120 will ignorethe existence of this neighboring node without considering a virtualrepulsive force from this neighboring node.

At S212, a net repulsive force Fi is calculated at the mobile node Nibased on location information received from neighboring nodes 140/120.In one example, the net repulsive force Fi equals a sum of virtualrepulsive forces applied by each neighboring node that is within athreshold distance from the mobile node Ni and whose messages can bereceived at the mobile node Ni, and the virtual repulsive forces by eachneighboring node are added by vector operations as in physics.Accordingly, the net repulsive force Fi applied on the mobile node Nican be represented as follows,

Fi=Σ _(j=1,f≠i) ^(M) Fij  (1)

where Fij represents a repulsive force applied on the mobile node Ni bya neighboring node Nj. The force Fij depends on a distance dij betweenthe two nodes Ni and Nj, and an orientation angle of Nj with respect toNi, and can be described by a polar coordinate notation (r, θ), where ris the magnitude and θ is the orientation angel. Specifically, the forceFij can be calculated using the following expression,

$\begin{matrix}{{Fij} = \left\{ \begin{matrix}{0,} & {{{if}\mspace{14mu} {dij}} \geq {Tr}} \\{\left( {{\frac{Wr}{Tr}\left( {{Tr} - {dij}} \right)},{\pi + a_{ij}}} \right),} & {{{if}\mspace{14mu} {dij}} < {Tr}}\end{matrix} \right.} & (2)\end{matrix}$

where Tr is the transmission range of the mobile nodes 140 in thedamaged area 160 that is used as a distance threshold to control howclose the two nodes Ni and Nj can be from each other, a_(ij) is the linesegment orientation angel from Ni to Nj, and w_(r) is a repulsive forcefactor. Accordingly, the repulsive force Fij is inversely proportionalto the distance dij between the two nodes Ni and Nj. When the distancedij is greater than the threshold distance, the repulsive force Fijequals zero, and no virtual repulsive force between the two nodes Ni andNj is considered.

As the deployed mobile nodes spread towards the disjoint segments 110a-110 d, a disjoint segment 110 a-110 d may become within thetransmission range of the deployed mobile nodes 140 and thus connectedto the deployed mobile nodes 140. Once a segment 110 a-110 d isconnected to the deployed mobile nodes 140, in order to stop expansionof the deployed mobile nodes 140 towards the connected segment 110 a-110d, the stationary nodes 120 at the edge of the connected segment 110a-110 d may exert repulsive forces towards the deployed mobile nodes 140within its transmission range. Thus, in some examples, when calculatingthe net repulsive force Fi for the node Ni using the expression (1) and(2), the stationary nodes 120 at the edge of connected segment 110 a-110d are also considered.

In a further example, a repulsive force F_(R) from a boundary of theapplication area 101 is added to the net repulsive force Fi when adeployed mobile node 140 reaches the boundary, thus limiting theexpansion of the deployed mobile nodes 140 within the application area.Accordingly, the net repulsive force Fi can be calculated using thefollowing expression,

Fi=F _(R)+Σ_(j=1,j≠i) ^(M) Fij  (3)

The repulsive force F_(R) can be calculated as in expression (2) where adistance between the node Ni and the boundary is used in place of dij,and an orientation angel of the line segment from Ni towards theboundary (the line segment is perpendicular to the boundary) is used inplace of a_(ij).

At S214, whether the net repulsive force Fi applied on the mobile nodeNi is smaller than a threshold is determined. When the net repulsiveforce Fi is smaller than the threshold, the process 200 proceeds toS222; otherwise, proceeds to S216.

At S216, a net movement distance is calculated based on the netrepulsive force Fi for the mobile node Ni. In one example, the netrepulsive force Fi calculated with expression (2) or (3) is used as thenet movement distance.

At S218, a location for the mobile node Ni to move to is determinedbased on a restricted movement distance. For example, when nodes arevery close to each other, the net repulsive force between them could bevery large, so the net move distance to move would be greater than thetransmission range Tr. Thus, in one example, the maximum movementdistance for each mobile node 140 is restricted to a restricted movementdistance equal to the transmission range Tr. Specifically, the location(x_(L), y_(L)) for the mobile node Ni to move from its current location(x_(i), y_(i)) is determined using the following expressions,

$\begin{matrix}{x_{L} = \left\{ \begin{matrix}{{x_{i} + \overset{\_}{X_{L}}},} & {\overset{\_}{X_{L}} < {Trx}} \\{{x_{i} + {Trx}},} & {\overset{\_}{X_{L}} > {Trx}}\end{matrix} \right.} & (4) \\{y_{L} = \left\{ \begin{matrix}{{y_{i} + \overset{\_}{Y_{L}}},} & {\overset{\_}{Y_{L}} < {Try}} \\{{y_{i} + {Try}},} & {\overset{\_}{Y_{L}} > {Try}}\end{matrix} \right.} & (5)\end{matrix}$

where X_(L) is the net distance to move in the direction of x-axis,Y_(L) is the net distance to move in the direction of y-axis, Trx=Trcos(θ), Try=Tr sin(θ), and θ is the net repulsive force orientationangle.

At S220, the mobile node Ni moves to the location determined at S218.Meanwhile, other mobile nodes 140 in the damaged area 160 also move tolocations determined in a process similar as the steps of S210-S220 forthe mobile node Ni. When movement of each mobile node 140 in the damagedarea 160 takes place, the balance of impulsive forces changesaccordingly among the mobile nodes 140. Then, a new iteration of thesteps for calculating a net repulsive force and determining a newlocation needs to be performed at the mobile node Ni. Accordingly, theprocess 200 returns to S210, and repeats.

At S222, whether net repulsive forces applied on each mobile node 140are smaller than the threshold is determined. For example, at eachmobile node 140, the step similar to S212 is performed, and a netrepulsive force applied to each mobile node 140 can be calculated. Theinformation of the calculated net repulsive forces can be transmitted toa control center, for example, through communications between the mobilenodes 140 and the base station 130 or between the mobile nodes 140 andthe deployment vehicle 150. The control center can determine whether netrepulsive forces applied on each mobile node 140 are smaller than thethreshold.

When the net repulsive forces applied on each mobile node 140 aresmaller than the threshold, it means that the mobile nodes 140 haveentered into a stable status and the spreading process 200 can bestopped. Accordingly, the process 200 proceeds to S299 and terminates atS299. On the other hand, when one of the net repulsive forces applied oneach mobile node 140 is larger than the threshold, the process 200continues at the mobile node Ni. Accordingly, the process 200 returns toS210 and is performed again. The result of the determination made at thecontrol center can be transmitted to the mobile node Ni and other mobilenodes 140, such that the mobile nodes 140 can subsequently take actionsto continue the process 200 or terminate it.

III. Distributed Dropping Approach for Mobile Nodes Placement

As shown in the FIG. 1 example, after partition of the WSAN 100 isdetected, a deployment vehicle is employed to drop additional mobilenodes 140 in the damaged area 160 to restore the connection of thedisjoint segments 110 a-110 d. The mobile nodes 140 spread over thedamaged area 160 based on the FBA as described above after beingdeployed, and eventually become uniformly distributed.

In the central dropping approach, multiple batches of mobile nodes areperiodically dropped in a central location within the damaged area 160,which disrupt the already-settled previously dropped mobile nodes. Forexample, newly deployed mobile nodes near the central location will pushpreviously deployed mobile nodes to move away from the central location.Consequently, total travelled distance of each deployed mobile node 140will increase continually until disjoint segments are reconnectedleading to continually increased power consumption of each mobile node140.

In one example, the distributed dropping approach is employed for mobilenode placement. In the distributed dropping approach, newly deployedbatches of mobile nodes are placed at locations away from the center ofthe damaged area 160, for example, to locations surrounding thepreviously deployed mobile nodes 140. In this way, the restorationprocess can be expedited and total travel distance and power consumptionof each mobile node 140 can be decreased compared with the centraldropping approach.

FIG. 3 shows an example of a mobile node placement process 300 utilizingthe distributed dropping approach. The process 300 includes nine steps(a) to (i) corresponding to the nine figures labeled with letters a toi, respectively, in FIG. 3. Accordingly, the nine figures are referencedas FIG. 3a to FIG. 3i , respectively. As shown in each of the figuresfrom FIG. 3a to FIG. 3b , a WSAN is partitioned into three disjointsegments 310 a-310 c, and multiple batches of mobile nodes 330-338 areplaced at certain locations in a damaged area 320 during the process300, for example, by a UAV. In one example, in each step (a) to (i), thedeployed mobile nodes spread over the damaged area 320 based on theabove FBA and enter a balanced status.

At step (a), a first batch of mobile nodes 330 is placed at a firstlocation (an initial location), for example, a central location or thecenter of the damaged area 320. Generally, the first location isselected to be a location leading to the most sufficient mobile nodeplacement solution according to some evaluation metrics, for example,total mobile node traveled distance, number of deployed mobile nodes,and the like. In some examples, a central location or the center of adamaged area is selected to be the first location for mobile nodeplacement. For example, in some situations, the locations of partitionedsegments and nodes within the partitioned segments are known after aWSAN is damaged. For such situations, the central location or center ofthe damaged area can be a location that has a minimum sum of distancesto borders of the partitioned segments. In other situations, thelocations of partitioned segments and nodes within the partitionedsegments are unknown after a WSAN is damaged, however, the border of theapplication area is known. For such situations, the central location orcenter of the damaged area can be a location which is the centroid orgeometric center of the damaged area. In one example, a central locationis known to all partitioned segments beforehand. In another example, thesurvived partitions can estimate a central location based on prioricommunications among partitioned segments before the WSAN ispartitioned.

After the deployment at the first location, batches of mobile nodes aresequentially deployed at locations surrounding the deployed mobilenodes. The locations surrounding the deployed mobile nodes are selectedbased on the distributed dropping approach, such that disruptions to thepreviously deployed mobile nodes are minimized. In FIG. 3 example,locations are determined to be on a circle with a radius of α·Trcentered on the initial location. Specifically, at step (b), a secondbatch of mobile nodes 331 is placed at a second location that is to theeast of the first location with a preconfigured distance denoted as α·Tr(α=1) where Tr is the transmission range of the deployed mobile nodes.At step (c), a third batch of mobile nodes 332 is placed at a thirdlocation that is to the northeast of the first location with the samedistance α ·Tr (α=1). At step (d), a fourth batch of mobile nodes 333 isplaced at a fourth location that is to the north of the first locationwith the same distance α·Tr (α=1). Similarly, from step (e) to step (i),a sequence of batches of mobile nodes 334-338 are sequentially placed atdifferent locations surrounding the first location. Specifically, thedifferent locations are locations to the northwest, west, southwest,south, south east of the first location corresponding to the figuresFIG. 3(e) to FIG. 3(i). In addition, the different locations are on acircle centered at the first location and having a radius equal to α·Tr(α=1).

After the steps (a) to (i) as illustrated in FIG. 3, the process 300 maycontinue in the following way if disconnected segments still exist. Forexample, additional batches of mobile nodes can be placed at locationslocated on a circle centered at the first location however with a radiusequal to α·Tr (α=2). In addition, the locations on the circle can be invarious directions from the first location. This process 300 may furthercontinues with a increasing gradually, for example, from 2 to 3, 4, . .. , and batches of mobile nodes are continually deployed aroundpreviously deployed mobile nodes.

During the above deployment process, the spreading mobile nodes mayreach a disjoint segment in a certain direction from the first location(for example, the mobile nodes are within a transmission range of astationary node within the disjoint segment). When this event occurs,the deployment of additional batches of mobile nodes at this directionwill be skipped. In other words, the mobile nodes will not be placed atlocations where a partitioned segment is connected to the deployedmobile nodes.

It is noted that the above example is only for illustration purpose. Thedistance between the central location and the locations for placingbatches of mobile nodes can be varied with various manners. For example,another distance configuration can be utilized other than thetransmission range Tr, and the factor α may change with other differentincrement values. In addition, locations for mobile node placement on acircle with the preconfigured distance may be determined in other waysinstead of eight directions evenly distributed on the circle.

III. Connectivity Restoration Approach in a Partitioned WSAN

In some examples, a connectivity restoration approach is employed toreconnect disjointed segments 110 a-110 d in the WSAN 100. Theconnectivity restoration approach is based on the above described FBAand distributed dropping approach. Two examples illustrating theconnectivity restoration approach are described below. The first exampleis described with reference to FIGS. 4 and 5, and the second example isdescribed with reference to FIG. 6.

FIG. 4 shows a polar representation of a process of dropping batches ofmobile nodes 140. In FIG. 4, the point O is the reference point (thepole of the polar coordinate system) representing an initial deploymentposition (e.g., the center of the damaged area 160 in FIG. 1 example),and the ray 401 is the reference direction (the polar axis). The point410 represents a position where a batch of mobile nodes is placed.Accordingly, the dropping process can be mathematically presented withthe following expressions,

S _(j) =A _(j)∠θ_(i)  (6)

A _(j) =α·Tr, α=1,2,  (7)

θ_(i) =iθ, i=1,2, . . . ,N _(s)  (8)

In the above expressions, S_(j) represents the position 410 in the formof polar coordinates, and A_(j) represents the distance between thereference point O and the position 410. The distance A_(j) is limited bya distance between the initial deployment location O and a nearestpartition in a specific orientation. In addition, as represented by theexpression (7), the distance A_(j) is expanded as the factor α variesduring a dropping process. Further, as represented by the expression(8), the orientation angle θ_(i) varies during a dropping process, andfor each round of dropping with an unchanged A_(j) value, the damagedarea is divided into a number (N_(s)) of equal sectors.

FIG. 5 shows an example of an algorithm 500 (in the form of pseudocode)for restoring disjoint segments 110 a-110 d in the WSAN 100. The polarrepresentation described with reference to FIG. 4 is used in thealgorithm.

At the beginning of the algorithm 500 as described in line 2, the factorα is set to be 1, and the orientation angle θ is set to 2π/Ns. Asdescribed by lines 3 and 8, the deployment of batches of mobile nodeswill continue until all disjointed segments are connected. Lines 3-7describe the process of deployment of the batches of mobile nodes.Specifically, corresponding to a certain value of the factor α, thedeployment is performed on locations at a circle with a radius of α·Tr,and the locations are in N_(s) different directions from the initialdeployment point O, as described by lines 3 and 4.

After each placement of a batch of mobile nodes, all deployed mobilenodes perform the FBA to spread over the damaged area 160 as describedby line 5. After the deployment on a circle with a certain value of thefactor α, the distance A_(j) is expanded as described by line 7.

FIG. 6 shows an example of a process 600 for restoring connectivity in apartitioned WSAN. FIG. 1 example is used for explanation of the process600. The process 600 starts at S601 and proceeds to S610.

At S610, an initial batch of mobile nodes is placed at a centrallocation of the damaged area 160 of the FIG. 1 example. For example,after a natural disaster event takes place, partition of the WSAN 100 isdetected, and the process 600 can be initiated. A deployment vehicle(e.g., a UAV) can be employed to place the first batch of mobile nodesat the center of the damaged area 160. After the deployment, the firstbatch of mobile nodes can spread based on the FBA and enter a stablestatus.

At S620, subsequent batches of mobile nodes can be sequentially placedat locations surrounding the previously deployed mobile nodes. Thedeployment can be based on the distributed dropping approach describedabove, and performed by the deployment vehicle 150 (e.g., a robot, aUAV, and the like). In one example, as described herein, the batches ofmobile nodes can be placed at locations on a circle centered at theinitial deployment location with a radius of a certain configured value(e.g., multiples of the transmission range of the mobile nodes). Thelocations for deployment can be in different directions from the initialdeployment location. In addition, at locations where a disjoint segmentis reconnected to the deployed mobile nodes, deployment of new mobilenodes will not be performed. In such a distributed dropping approach,the disruption by the newly deployed mobile nodes on the previouslydeployed mobile nodes can be decreased compared to the central droppingapproach in which mobile nodes are deployed on the initial deploymentlocation.

At S630, the batches of mobile nodes deployed at S620 are spread overthe damaged area 160 based on the FBA. For example, each deployed mobilenode can perform a spreading process based on the FBA until all deployedmobile nodes enter a balanced status. During the spreading process, adisjoint segment may be connected to the deployed mobile nodes,information of which can be transferred to a control center, forexample, through a base station.

In another example, information of reconnection of a disjoint segment istransmitted to the deployment vehicle 150, such that the deploymentvehicle 150 knows about locations where a segment is connected to thedeployed mobile nodes, and a next round of mobile node placement will beskipped at the respective locations.

At S640, whether connectivity among the partitioned segments has beenrestored is determined, for example, by the control center, based on thereconnection information received from the base station 130. When thereare still disconnected segments to be connected, the process 600 returnsto S620. In one example, the control center transmits a message to thedeployment vehicle 150 to inform the result of the determination, suchthat a next round of deployment can be performed. In another example, adeployment vehicle can be used to perform the step of S640 to make thedetermination instead of the control center. When it is determined thatall segments have been reconnected, the process proceeds to S640, andterminates at S640.

While aspects of the present disclosure have been described inconjunction with the specific embodiments thereof that are proposed asexamples, alternatives, modifications, and variations to the examplesmay be made. Accordingly, embodiments as set forth herein are intendedto be illustrative and not limiting. There are changes that may be madewithout departing from the scope of the claims set forth below.

1: A method for restoring connectivity among partitioned segmentsdisjoint with each other in a wireless sensor and actor network (WSAN),comprising: placing an initial batch of mobile nodes at an initiallocation within a damaged area of the WSAN, and spreading the initialbatch of mobile nodes, wherein the spreading is by a force basedcalculation of a net repulsive force determined from magnetic polesassigned to each node of the batch of mobile nodes; placing firstbatches of mobile nodes at first locations on a first circle centered atthe initial location with a first radius, and spreading the firstbatches of mobile nodes; placing a second batch of mobile nodes at asecond location on a second circle centered at the initial location witha second radius that is larger than the first radius, and spreading thesecond batch of mobile nodes; determining whether connectivity among thepartitioned segments has been restored; and when connectivity among thepartitioned segments is not restored, placing additional batches ofmobile nodes surrounding previously placed mobile nodes. 2: The methodof claim 1, wherein the second location on the second circle is within atransmission range of the previously placed first batches of mobilenodes. 3: The method of claim 1, further comprising: placing batches ofmobile nodes at locations surrounding previously placed mobile nodesexcluding locations where one of the partitioned segments is connectedto the previously placed mobile nodes within the damaged area of thepartitioned WSAN. 4-5. (canceled) 6: The method of claim 1, furthercomprising: placing a third batch of mobile nodes at a third locationsurrounding the previously placed mobile nodes placed within the damagedarea of the partitioned WSAN; spreading the third batch of mobile nodes;and placing a fourth batch of mobile nodes at a fourth locationsurrounding the previously placed mobile nodes placed within the damagedarea of the partitioned WSAN. 7-20. (canceled)